This section provides additional information concerning the Method. For the general design, please refer to the main text.
If you want to replicate the experiment, you will find the
code for the experiment and also a file
(How to conduct the experiment.docx) explaining steps by
step how to proceed in the folder Program_Experiment in my
github:
mathjoss/ExpCommunityVariation.
56 participants participated in this study (38 women and 18 men). They were between the ages of 18 and 50 (M= 24, SD=5 ). Please refer to Participants’ characteristics to see more about the distribution of age, gender, and other measures.
The setup is composed of four tables (labeled “A,” “B,” “C,” and “D”), each hosting a computer. Tables “A” and “C” are facing each other, and tables “B” and “D” too. Curtains are placed between the pair of table AC and BD to prevent the pairs of individuals sitting at one block of table from observing those at another. Stickers are affixed to the computer keyboards to indicate which keys participants can press. Following each round, two out of the four participants switch tables, taking their computers with them. The designated table to which they need to go is specified both in the computer program and on a piece of paper attached to the computer. The laptops are placed on a rotating device, which makes it easier for the participant to rotate their screen. When they arrived to the room, the first thing they do is to read and sign the consent form. Participants were paid 21 euros for their participation.
Stimuli were squares of size 300*300 pixel when being presented the 8 together, and 400*400 pixel the rest of the time.
Here are presented the instructions for each part.
Passive exposure: Dadelijk zie je een aantal afbeeldingen een voor een op het scherm verschijnen samen met het woord in fantasietaal dat die afbeelding beschrijft. Probeer zo goed mogelijk het juiste woord bij elke afbeelding te onthouden.
First Testing (Round 0): Nu is het tijd om te testen hoe goed je de fantasietaal onthoudt! U ziet dezelfde afbeeldingen. Denk goed na over hoe je ze een naam zou geven en druk op enter als je klaar bent om te typen (tijdens het typen kun je de scene niet meer zien). Maak je geen zorgen als je de naam van de afbeelding niet meer weet en beproef je geluk door een woord te typen.
Communication game, Guesser: Je partner heeft een afbeelding gezien en een woord getypt om het te beschrijven. Lees het woord op de computer van je partner en kies de juiste afbeelding uit de 8 mogelijke afbeeldingen (gebruik 1-2-3-4-5-6-7-8 op het toetsenbord om een keuze te maken). Je krijgt feedback over je keuze, probeer er van te leren. Maak tijdens het experiment zo min mogelijk fouten! Vergeet niet om de feedback aan je partner te laten zien. Je krijgt feedback over je keuze, probeer daarvan te leren
Communication game, Producer: Nu krijg je een afbeelding te zien. Denk na over hoe je het zou noemen en druk op Enter als je klaar bent om te typen. Als je klaar bent met het schrijven van het woord, druk je nogmaals op enter en draai je de computer zodat je partner het woord kan lezen en kan raden welke afbeelding je beschrijft. Tijdens deze taak mag je de taal niet wijzigen naar Nederlands of andere bestaande talen. Gebruik ook niets dat heel erg op het Nederlands of andere talen lijkt. Ook mag je geen Nederlandse afkortingen, afkortingen of acroniemen gebruiken. Let op, je kunt niet alle letters gebruiken: alleen de letters die zichtbaar zijn op het toetsenbord kunnen worden gebruikt.
Testing (Round 10): Nu hoef je niet meer met je partner te communiceren. U moet een reeks afbeeldingen een naam geven in de nieuwe taal die u gebruikte.
When we first designed the experiment, participants had greater exposure to the initial labels (2 exposure of 8 seconds each, compared to 1 exposure of 7 second in the final design). During the pre-test, we observed very high recall of these labels. We found that participants showed no flexibility when they were too well-trained and tended to stick to the initial labels.
We made slight adjustments to the design to reduce participants’ memory of the labels, allowing us to observe flexibility and language change.
It is worth noting that an experimental design with no exposure to initial labels is also possible, although it would introduce additional constraints in terms of experiment management.
We also conducted another pre-test where the experimenter made an error when asking participants to switch seats. As a result, we excluded this data from the analysis. [Note: the results from this group were consistent with our hypothesis, showing adaptation to the biased participant]
All measures are described within the results.
The study included three additional tasks.
This version of the Dictator Game is adapted in the context of the experiment. We included this task as another way to measure prosociality. Participants were presented with the following fictional situation:
English version:
Imagine that I give you an additional amount of 100 euros due to the excellent performance of your group during this experiment. Now, you have the choice to keep the full amount for yourself or to share it with the other participants. Since the other participants are not aware of this extra reward, the choice is entirely up to you. How much do you decide to share with the other participants?
They had the choice between:
Dutch version:
Stel je voor dat ik je een extra bedrag van 100 euro geef vanwege de uitstekende prestaties van jouw groep tijdens dit experiment. Nu heb je de keuze om het volledige bedrag voor jezelf te houden, of het te delen met de andere deelnemers. Aangezien de andere deelnemers niet op de hoogte zijn van deze extra beloning, is de keuze geheel aan jou. Hoeveel besluit je te delen met de andere deelnemers?
The task-switching experiment adapted from Roger and Monsell’s paradigm. An online version is available to try at this address: https://www.psytoolkit.org/experiment-library/taskswitching.html
The code of the task-switching experiment and the prosociality experiment are all available in the same file as for the code of the main experiment (see my github: mathjoss/ExpCommunityVariation).
Throughout the results, we will use the following terminology:
Group: when using the terminology “for each group”, I will mean for each group of 4 that came to the lab. In the R data, we used several variables: GroupNum refers to the number of the group (e.g, 1, 2, 3, 4, 5, 6, 7), GroupType refers to the type of the group (control versus homogenous), and GroupID is the combination of the two (1_Control, 2_Control…, 1_Hetero.., 7_Hetero). When saying “for each group”, I implicitely imply “for each GroupID”.
Initial labels refers to the 8 initial words used to describe aliens presented in the passive exposure phase (aike, nusa, …)
Unbiased participants are participants 2, 3, and 4 (who can produce all letters) and biased participant refers to participant 1 (who cannot produce a and k). This is consistent across all groups.
Unbiased letters designate letters who can be produced by all participants (p, s, n, e, i, u) and biased letters designate the 2 letters that cannot be produced by the biased participants (k, a)
Typographic conventions:
variable names is represented using italic text
emphasis is represented using bold text
software, programming concepts, or
files/folders' name (e.g., applications, packages or
function names) are represented using
fixed font text
We proceed and clean the files using the following methods:
After each group passation, we use CleanUpFiles.R (see
folder InputFiles of my github folder github:
mathjoss/ExpCommunityVariation) to perform the following steps:
Data. merge the dataset obtained from the 4 participants into 1 single file using the R script
Prosociality. For each participant, we compute the total prosociality score by additionning the results on each question
Inverse efficiency. For each participant, we compute the inverse efficiency, where inverse efficiency is defined as \(mean(time)/mean(accuracy)\)
Cognitive Flexibility. We measure each participant’s cognitive flexibility by examining their performance in a task that involves both numbers and letters. To do this, we calculate two average times: one for when the participant does not switch tasks (moving between letters or numbers) and another for when they do switch tasks (moving from numbers to letters or vice versa). The difference between these two averages represents their cognitive flexibility. We further normalize this difference by dividing it by the mean time required for task switching.
The “data” files are named after the group number and type, and it is saved as a .csv file. For instance, Group1HT.csv represents the data file for Group 1 Heterogenous.
The “other” measures (prosociality, inverse
efficiency, cognitive flexibility) are summarized in a separate data
file starting with Other_Group…, which includes the group
number and type. This file also contains information about
age, gender, and results in the
dictator game.
We merge datasets from all groups, thus obtaining two datasets:
GroupNum GroupType TypeTest Producer Guesser
1:832 Control:2912 ComGame :4032 1:1456 1 :1008
2:832 Hetero :2912 FirstTesting : 448 2:1456 2 :1008
3:832 PassiveExposure: 896 3:1456 3 :1008
4:832 SecondTesting : 448 4:1456 4 :1008
5:832 NA's:1792
6:832
7:832
Round Shape ACC Word
Min. : 0.000 aike : 728 Min. :0.0000 Length:5824
1st Qu.: 1.000 anap : 728 1st Qu.:0.0000 Class :character
Median : 4.000 esip : 728 Median :1.0000 Mode :character
Mean : 4.231 kesip : 728 Mean :0.6772
3rd Qu.: 7.000 nekuki : 728 3rd Qu.:1.0000
Max. :10.000 nus : 728 Max. :1.0000
(Other):1456 NA's :1344
ID_CG index pair GroupID ProducSim
Min. :0.000 Min. : 1.00 1_2 : 672 1_Control: 416 Min. :0.0000
1st Qu.:0.000 1st Qu.: 28.75 1_3 : 672 1_Hetero : 416 1st Qu.:0.5000
Median :2.000 Median : 80.50 1_4 : 672 2_Control: 416 Median :1.0000
Mean :2.423 Mean : 82.96 2_3 : 672 2_Hetero : 416 Mean :0.7482
3rd Qu.:5.000 3rd Qu.:132.25 2_4 : 672 3_Control: 416 3rd Qu.:1.0000
Max. :7.000 Max. :176.00 3_4 : 672 3_Hetero : 416 Max. :1.0000
NA's:1792 (Other) :3328
PartID GroupNum prosoc DictatorGame Age
Min. :1.00 Min. :1 Min. :1.812 Min. :1.000 Min. :18.00
1st Qu.:1.75 1st Qu.:2 1st Qu.:3.500 1st Qu.:3.000 1st Qu.:20.00
Median :2.50 Median :4 Median :3.812 Median :3.000 Median :23.00
Mean :2.50 Mean :4 Mean :3.714 Mean :2.786 Mean :24.02
3rd Qu.:3.25 3rd Qu.:6 3rd Qu.:4.062 3rd Qu.:3.000 3rd Qu.:27.00
Max. :4.00 Max. :7 Max. :4.438 Max. :5.000 Max. :37.00
Gender WorkingMem difference CogFlexibility
Length:56 Min. :1.061 Min. :-1.0784 Min. :-0.6577
Class :character 1st Qu.:1.301 1st Qu.: 0.3999 1st Qu.: 0.2424
Mode :character Median :1.551 Median : 0.5361 Median : 0.3271
Mean :1.695 Mean : 0.6125 Mean : 0.3164
3rd Qu.:1.863 3rd Qu.: 0.8278 3rd Qu.: 0.4237
Max. :3.324 Max. : 2.0339 Max. : 0.6110
GroupType
Length:56
Class :character
Mode :character
We look at the productions during the FirstTesting and the last testing (called here SecondTesting). As a reminder, FirstTesting occurs after the passive exposure, and SecondTesting occurs after the communication game.
Group 1:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | uine | unip | esip | nesi | nesipi | nus | nuse | inus |
| 2 | suka | nuki | pasip | nusip | pikak | nup | nuki | nukik |
| 3 | aike | akin | sepik | kipe | nekuki | nus | nusa | peki |
| 4 | paik | piak | esup | nenusa | nekuki | nus | nusa | piak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | pine | enup | esip | nenuse | nepipi | nus | nuse | puni |
| 2 | paik | esup | esip | nanusip | nukeki | nuk | suka | ekip |
| 3 | paik | kusip | esip | nenusa | nenuki | nus | nusa | nuki |
| 4 | paik | sanip | esip | nenusa | nenuka | nus | nusa | senip |
Group 2:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipe | unup | esip | nesip | nepupi | esu | nusu | puei |
| 2 | aike | upak | esip | kesip | nusa | nusa | nusa | puak |
| 3 | anap | anap | esip | kesip | nekuki | nus | nusa | puak |
| 4 | aike | kusap | esi | kesi | sup | nus | nuk | nuki |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipe | unup | esip | nesip | nepupi | nus | nusu | pue |
| 2 | aike | anap | pua | kesip | kukupa | nus | nusa | pua |
| 3 | aike | anap | esip | kesip | nekuki | nus | nusa | pua |
| 4 | aike | anap | esip | kesip | kukupa | nus | nusa | pua |
Group 3:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | ie | ee | nus | en | neiu | nus | nus | pu |
| 2 | aike | anap | kesip | enis | nukaki | nus | esip | nesip |
| 3 | enik | anak | naku | kesin | enik | nus | nusa | nekuki |
| 4 | aike | anap | esip | kesip | nekuki | nuak | nusa | nuak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | ie | nus | esip | esip | nuui | nus | nus | pu |
| 2 | aike | anap | esip | uiuie | nukaki | nus | nusp | iesie |
| 3 | suki | nupa | esip | kesip | nekuki | nus | nusa | nekiki |
| 4 | aike | anap | esip | kesip | nekuki | nus | nusa | nuak |
Group 4:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | ie | np | nesis | esis | neui | nus | ns | pien |
| 2 | puak | asap | esip | kesip | puak | nup | nuki | puak |
| 3 | aike | enus | sup | esun | kuapa | esip | enus | kaup |
| 4 | aike | anap | nusa | aise | nepik | nus | anap | puak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | inp | enep | uinus | inus | nepupi | nus | ienies | pieu |
| 2 | aike | asap | pieu | kessip | nepupi | nup | inus | puak |
| 3 | aike | esep | unus | enus | nekip | nus | inus | kaup |
| 4 | aike | anap | kisa | kessip | nekip | nus | nusa | puak |
Group 5:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | ie | np | esip | eip | nus | nus | pu | |
| 2 | una | esip | una | sunua | nukaki | esip | kika | esep |
| 3 | aike | nesip | esip | nesip | nuas | kapu | nuap | nakuku |
| 4 | aike | euki | esip | apak | nekuki | nup | asep | isap |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | ie | np | esip | esipp | nusinu | nupi | nus | inis |
| 2 | aike | np | epik | sesss | kasaki | usa | nup | usa |
| 3 | aike | supi | esip | sess | nakuki | nup | nus | np |
| 4 | aike | np | esip | esipppp | nukaki | nuk | ss | epik |
Group 6:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | esei | enep | nuis | senui | nus | nusi | nesupi | |
| 2 | aike | anap | esip | kesip | nekuki | nun | nusa | puak |
| 3 | aike | anap | esip | sekin | nekuki | sap | nusa | puak |
| 4 | peki | ani | sunak | nekaki | nusaki | nuk | nekaki | nusak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipi | enep | epui | puise | pepupi | nuse | nus | epei |
| 2 | aike | anap | seki | kesip | nekuki | nan | nusa | puak |
| 3 | aike | anap | seki | esip | nekuki | nak | nusa | puak |
| 4 | kuap | ani | nekaki | epi | nesaki | suk | peike | kuap |
Group 7:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | in | n | pui | nu | nu | nus | ui | n |
| 2 | aike | anap | esip | kapu | nekuki | asap | nusa | naku |
| 3 | aike | anas | esip | nesip | nekuki | nus | nusa | puki |
| 4 | enke | apa | ekip | esnik | a | ip | ana | pun |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipe | nesu | epin | pine | neipe | nus | nusu | sinu |
| 2 | aike | anas | nekip | pinu | nekuki | nus | nusa | senu |
| 3 | aike | anas | nukip | pinu | nuipe | nus | nusa | seni |
| 4 | pike | anas | enpik | enpiku | nipuki | nus | nusa | pine |
Group 1:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | akap | esip | kesip | nekuki | nue | isip | ekup |
| 2 | aike | usap | aise | pasu | nekaki | pasu | nasu | nesu |
| 3 | aike | puak | puak | kesip | nekuki | nus | nusa | anani |
| 4 | aike | anap | esip | kesip | nakuki | nus | nusa | pusa |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nekuki | nuk | nusa | puak |
| 2 | aike | anu | espi | kesip | nekuki | nuk | nusa | puak |
| 3 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
| 4 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
Group 2:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | puak | nepik | nekip | pekuke | nus | puek | ekip |
| 2 | aupi | anaap | neuik | kesip | nekuki | nus | nus | auki |
| 3 | aike | apap | esip | kepip | nekuke | nunu | anuna | esip |
| 4 | aike | enuik | espin | nesu | pinak | nus | nusa | puak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | asap | peuk | kesip | nekuki | nus | nuna | kapi |
| 2 | ausi | asap | peuk | kesip | nekuki | nus | nuna | ausi |
| 3 | aike | asap | puki | kesip | nekuki | nus | nuna | puik |
| 4 | aike | asap | sik | puik | akunu | nus | nuna | suipe |
Group 3:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nukuki | nus | nusa | pinuk |
| 2 | aine | anep | esip | kesip | anaki | nus | kanip | anap |
| 3 | aike | anapi | nuas | neki | nekuki | nus | nuas | puas |
| 4 | aspe | anak | enis | nusa | nekuki | epis | suki | pua |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | nap | esip | kesip | nukuki | nus | nusa | pusip |
| 2 | aike | anasp | esip | kesip | nekuki | nus | nusa | puaki |
| 3 | aike | anasp | esip | kesip | nekuki | nus | nusa | puaki |
| 4 | aike | anasp | esip | kesip | nekuki | nus | nusa | puaki |
Group 4:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | puka | kesip | nekuki | nus | nusa | esip |
| 2 | aike | anak | esip | kesip | nukiki | nus | nusa | puak |
| 3 | asip | anap | esip | keniki | keniki | nupu | pasu | esik |
| 4 | puaki | anap | nuk | kuni | pukaki | nus | nusa | puak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nekiki | nus | nusa | puak |
| 2 | aike | anap | esip | kesip | nanuki | nus | nusa | puak |
| 3 | aike | anap | esip | kesip | kanuki | nus | unsa | puka |
| 4 | aike | anap | esip | kesip | nekiki | nus | nusa | puak |
Group 5:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nekuki | nus | nusa | kuak |
| 2 | kesi | anap | pusa | kesip | kununa | nap | nepi | kupi |
| 3 | aike | asap | esip | kesip | nekusi | nus | enis | pnua |
| 4 | aike | anak | esip | esip | nekuki | nus | nusa | puak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
| 2 | nues | napa | esip | kesip | nekuki | nus | nusa | puak |
| 3 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
| 4 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
Group 6:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | enap | esip | kesip | nekuki | nus | nusa | puak |
| 2 | esai | punke | esip | enku | nekuki | nusa | nusa | akik |
| 3 | uas | anap | puki | sekip | nekuki | nas | auke | suki |
| 4 | aike | kesip | aike | kesip | kusseni | esip | nusa | puak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | enap | esip | kesip | nekuki | nus | nusa | ipuk |
| 2 | aike | enap | esip | kesip | nekuki | nus | nasu | paku |
| 3 | aike | enap | esip | kesip | nekuki | nus | nusa | paku |
| 4 | aike | enap | esip | kesip | nekuki | nus | nusa | puka |
Group 7:
Before training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | asap | esip | keisa | nekuki | nus | nusa | aike |
| 2 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
| 3 | aike | nus | nusip | kuap | nekuki | nusa | nesip | kuap |
| 4 | aike | anap | esip | kesip | nekuki | nus | nusa | kuak |
After training:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | aike | anap | esip | kesip | nekuki | nus | nusa | puas |
| 2 | aike | asap | esip | kesip | nekuki | nus | nusa | puak |
| 3 | aike | anap | esip | kesip | nekuki | nus | nusa | kuap |
| 4 | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
Here, we examine how well the participants remembered the initial labels for the images, looking at the labels written by the participants during the FirstTesting.
Accuracy is binary: a value of 1 indicates correct recall by the participant, while a value of 0 signifies the presence of at least one error. However, we made an exception for the biased participant. In their case, their responses were considered “correct” if they substituted the biased letter they were unable to produce with another letter, or if they omitted it. Please note that for the biased participant in the heterogeneous groups, we manually coded the accuracy, only for the pre-communication (round 0) testing moment. Indeed, we only look at this measure in this context.
Participants were presented with the following initial labels during the passive exposure phase: kesip, esip, nusa, nus, aike, puak, nekuki, and anap. Our analysis focuses on the differences between participants’ first productions (during FirstTesting) and the initial labels. To do this, we computed the normalized Levenshtein distance between the initial labels and the initial productions. Please note that we tried to find a way to compute an exception for the biased participant, in a similar way as we did for the learning accuracy. However, we could not find a solution that would not “advantage” or “disandvantage” the biased participant. Thus, when plotting the results from the initial production similarity, we removed the biased participant, in order to have two sets of data which are comparable.
Figure 1. Learning success (accuracy on the left, initial production similarity on the right) per group type. Dots indicate each participant. The red dot shows the mean of the group, and red point range shows the standard error.
Participants remembered in average 47.1% of the initial labels, with a standard deviation of 27.18. The average production similarity with the initial labels is of 0.67 with a standard-deviation of 0.2.
We check whether the difference of learning is statistically different. This is not an hypothesis, just a sanity check that our two group types are similar.
With accuracy learning:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_acc ~ GroupType + (1 | GroupID)
Data: df_agg_acc
REML criterion at convergence: 515.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.57025 -0.73141 -0.06612 0.85951 1.78513
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.0 0.00
Residual 729.5 27.01
Number of obs: 56, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 51.786 5.104 54.000 10.146 4.09e-14 ***
GroupTypeHetero -9.375 7.218 54.000 -1.299 0.2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
GroupTypHtr -0.707
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
With initial production similarity: (please note that here, we look at a model that include all productions from the control groups, but only production from participant 2, 3, and 4 in the heterogenous groups, since the biased compared cannot be directly compared to them).
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_lev_dis ~ GroupType + (1 | GroupID)
Data: df_agg_dist2
REML criterion at convergence: -12.6
Scaled residuals:
Min 1Q Median 3Q Max
-2.3659 -0.7941 -0.1304 0.9421 1.7428
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.00000 0.0000
Residual 0.03911 0.1978
Number of obs: 49, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.70704 0.03737 47.00000 18.919 <2e-16 ***
GroupTypeHetero -0.09335 0.05709 47.00000 -1.635 0.109
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
GroupTypHtr -0.655
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
-> The learning difference between the two groups is not significant
Looking at each shape:
Figure 2. Levenshtein distance between initial words and initial productions for each word. Blue dots show biased participants.
Figure 3. Distribution of the scores. Red shows the results for the control group, blue shows the results for the heterogenous group.
When building t-tests comparing each of these characteristics for the groups, we obtain the following p-values (please note that we used a chisq test for gender):
None of these values are significant, except for the distance to initial words. This can be easily explained given that the method we used to measure the initial production similarities is different for biased and unbiased participants. Thus, if we remove the biased participants, this p-value is not-significant anymore: 0.3.
In this part, we only look at the patterns observed in the heterogenous groups.
What are the strategies used by the biased participant to produce the initial labels before communicating? In this table, we count the number of times each biased participant has performed:
removal means that the biased participant remembered the label, and decided to remove the biased letter
switch means that the biased participant remembered the label, and decided to switch the biased letter with another unbiased letter
forgot means that the biased participant has forgot the initial label
| removal | forgot | switch | |
|---|---|---|---|
| Group1 | 0 | 1 | 5 |
| Group2 | 0 | 0 | 6 |
| Group3 | 4 | 2 | 0 |
| Group4 | 5 | 1 | 0 |
| Group5 | 5 | 1 | 0 |
| Group6 | 0 | 4 | 2 |
| Group7 | 0 | 6 | 0 |
Please note that these tables were filled manually.
Then, we also look at the pattern presented by the biased participant after communicating. How did this biased participant produce the label? Did this participant:
removal: used the initial label, but removed the biased letter
switch: used the initial label, but switched the biased letter with another unbiased letter (please note that in the case of “nekuki” label, we consider as “switch” things like “nepupi” or “nepipi”; it is not exactly the same word so it should be considered in the “new” column, but we think that the strategy is actually a switch (+ a weak forgot))
new: adopted a new label
special: here to condition where the participant has removed the biased letter, but has also added a letter at the end of the word. Then, the word was identifiable by the other members of the groups by the addition of this final letter (for example, esipp, and other participants produced esippp, sesss, sessss).
| removal | new | switch | special | |
|---|---|---|---|---|
| Group1 | 0 | 1 | 5 | 0 |
| Group2 | 0 | 6 | 0 | 0 |
| Group3 | 5 | 0 | 1 | 0 |
| Group4 | 0 | 2 | 4 | 0 |
| Group5 | 3 | 1 | 1 | 1 |
| Group6 | 1 | 3 | 2 | 0 |
| Group7 | 0 | 4 | 2 | 0 |
These tables concerned only the biased participants. We can also look at the productions of the unbiased participants after they communicated (during the final testing) to look at their adaptative strategy. Please note that we only look here at the labels featuring one or two biased letters (all labels but nus and esip). Here are the following possible options:
SameBiased_Removed: used the same label as the biased participant, in the case where the biased participant has removed a biased letter
SameBiased_Removed: used the same label as the biased participant, in the case where the biased participant has switched a biased letter with another unbiased letter
SameBiased_New: used the same label as the biased participant, in the case where the biased participant has created a new label
InitialLabel: used the initial label, even if the biased participant cannot use it the same way
DiffBiased_Adapt: use a different label from the biased participant, however this new label does not feature biased letter
DiffBiased_ABitAdapt: use a different label from the biased participant, this new label features slightly less biased letters than the original label (namely, instead of 2 biased letters, there is only one biased letter)
DiffBiased_NonAdapt: use a different label from the biased participant and from the initial label, featuring biased letters
| SameBiased_Removed | SameBiased_Switch | SameBiased_New | InitialLabel | DiffBiased_Adapt | DiffBiased_ABitAdapt | DiffBiased_NonAdapt | |
|---|---|---|---|---|---|---|---|
| Group1 | 0 | 0 | 0 | 2 | 2 | 5 | 9 |
| Group2 | 0 | 0 | 0 | 14 | 0 | 3 | 2 |
| Group3 | 0 | 0 | 0 | 10 | 2 | 3 | 3 |
| Group4 | 0 | 1 | 0 | 7 | 4 | 2 | 4 |
| Group5 | 3 | 0 | 0 | 3 | 7 | 2 | 3 |
| Group6 | 0 | 0 | 0 | 11 | 0 | 2 | 5 |
| Group7 | 0 | 0 | 0 | 6 | 6 | 2 | 4 |
When adapating, there are three main types of strategy used by the unbiased participants to adapt to the biased participants:
either they use the same word as the biased participant (it has happened 4 times out of the 6 words containing a biased letter and the 21 unbiased participants -> total of 126 occurences).
either they use a new label, not used by the biased participants, but that does not feature any biased letters: 21 or that does feature less biased letters than the original label: 19
If they do not adapt, either by using the initial label that contains as many biased letters as the original label (or more): 83
learning performance (both using accuracy index and distance to initial learning) are similar between control and heterogenous groups
some words are easier to remember compared to other (such as aike or nus)
the participant characteristics are similar between control and heterogenous groups (in average, they have approximately the same age, but also personal characteristics such as working memory, cognitive flexibility…)
in order to compensate for their difference, biased participants either remove the biased letter(s) or switch them to another letter. After communicating, they also come up with new words
unbiased participants adapt mostly by using another label which does not feature any biased letter (or less frequently), and sometimes they adapt by copying the label used by the biased participant
In this part, we will find the plots and the models that are referred in the main paper as:
Here, we examine the level of communicative success in interactions, specifically distinguishing between successful (success=1) and unsuccessful (success= 0) interaction in pairs. Please note that the variables Round2 here is the reverse order of Round (so that Round 9 becomes Round 0).
We look at the evolution of communicative success for each group:
Figure 4. Evolution of communicative success for each group.
We can see that the communicative success of group 2 in the heterogeneous group is particularly high.
Let’s look at the aggregated performance for each group type:
Figure 5. Evolution of communicative success aggregated by group type: control or heterogenous.
These plots raise two questions:
Is there a significant improvement of communicative success with time?
Is there a significant difference of communicative success between heterogeneous and control groups?
To investigate these questions, we build a linear mixed-effect models using the group type (hetero versus control) and the round as fixed effect. We use the aggregated data by pair, and we control for the random effect of Group Number.
Model 1:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_acc ~ GroupType * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: 2082.6
Scaled residuals:
Min 1Q Median 3Q Max
-3.3675 -0.5828 -0.0625 0.7277 3.4084
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 149.1 12.21
Residual 208.4 14.43
Number of obs: 252, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 102.3512 5.1882 16.4845 19.728 6.75e-13 ***
GroupTypeHetero -27.8571 7.3373 16.4845 -3.797 0.00151 **
Round2 -5.1265 0.4980 236.0000 -10.293 < 2e-16 ***
GroupTypeHetero:Round2 1.0491 0.7043 236.0000 1.489 0.13770
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH Round2
GroupTypHtr -0.707
Round2 -0.384 0.272
GrpTypHt:R2 0.272 -0.384 -0.707
We also used a model in which data is not aggregated by pair. In this new model, we also added a random effect for pair. The results of the model are very similar, but show even stronger effects.
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula: ACC ~ GroupType * Round2 + (1 | GroupID) + (1 | pair)
Data: df2
AIC BIC logLik deviance df.resid
4061.5 4099.3 -2024.8 4049.5 4026
Scaled residuals:
Min 1Q Median 3Q Max
-9.1003 -0.7776 0.2886 0.6434 1.8459
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.47217 0.6871
pair (Intercept) 0.01215 0.1102
Number of obs: 4032, groups: GroupID, 14; pair, 6
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.70442 0.31978 11.584 < 2e-16 ***
GroupTypeHetero -2.54209 0.41995 -6.053 1.42e-09 ***
Round2 -0.43406 0.03037 -14.295 < 2e-16 ***
GroupTypeHetero:Round2 0.24810 0.03568 6.953 3.57e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH Round2
GroupTypHtr -0.744
Round2 -0.526 0.396
GrpTypHt:R2 0.442 -0.439 -0.837
There is a significant improvement in performance with time in both group type (control and heterogenous), as shown by the main effect of the Round2 variable. A lower performance is observed in the heterogenous groups than in the control group, as shown by the main effect of the GroupType variable depsite the very high performance reached by heterogenous Group 2. Moreover, no interaction effect between group type and round is present.
From this analysis, it is clear that the average communicative success is lower in heterogeneous groups compared to control groups. However, it could be due to the fact that heterogeneous groups include interactions with a biased participants. Thus, it is interesting to split the heterogeneous groups into two categories:
Hetero_biased (pairs in the heterogeneous groups involving the biased participant: 1-2, 1-3, 1-4)
Hetero_nonbiased (pairs in the heterogeneous groups that do not involve the biased participant: 2-3, 2-4, 3-4).
This could lead to two different scenarios:
Hetero_nonbiased has high communicative success similarly to control groups, because these pairs do not include the biased participants ;
The confusion introduced by the biased participant spread to all participants, and the performance of hetero_unbiased is still lower than for control groups.
Figure 6. Same as above, except that here we split heterogenous groups in 2: pairs including the biased participant and pairs without the biased participant.
The plot suggests that hypothesis 2 is supported: the presence of the biased participant has introduced confusion within the heterogeneous group, leading to a decrease in the communicative success even in interactions between unbiased participants. However, in general, the pair with the biased individual seems to achieve an even lower accuracy score (in the heterogenous group). We used a mixed-effect model to see if this is statistically significant (this refers to the model 1 bis of the main paper:)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_acc ~ type * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: 2060.2
Scaled residuals:
Min 1Q Median 3Q Max
-3.4762 -0.6021 -0.0308 0.7018 3.1542
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 149.8 12.24
Residual 195.5 13.98
Number of obs: 252, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 102.3512 5.1646 16.1891 19.818 8.84e-13
typeHetero With Biased -32.8274 7.6565 19.4992 -4.288 0.000378
typeHetero Without Biased -22.8869 7.6565 19.4992 -2.989 0.007391
Round2 -5.1265 0.4825 234.0000 -10.626 < 2e-16
typeHetero With Biased:Round2 0.9896 0.8356 234.0000 1.184 0.237530
typeHetero Without Biased:Round2 1.1086 0.8356 234.0000 1.327 0.185909
(Intercept) ***
typeHetero With Biased ***
typeHetero Without Biased **
Round2 ***
typeHetero With Biased:Round2
typeHetero Without Biased:Round2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) typHtrWthBs typHtrWthtB Round2 typeHtrWthBsd:Rnd2
typHtrWthBs -0.675
typHtrWthtB -0.675 0.820
Round2 -0.374 0.252 0.252
typeHtrWthBsd:Rnd2 0.216 -0.437 -0.146 -0.577
typHtrWthtBsd:Rnd2 0.216 -0.146 -0.437 -0.577 0.333
Let’s just compare the pairs with the biased participant to the pairs without. Note that pairs with the biased participants are considered to be the pairs involving participant 1 even in the control groups. This allows us to check that there is no difference between these “sham” biased pairs and the other pairs in the control groups.
Figure 7. Mean communicative success for each group, whether unbiased communicate with biased participant (part 1) or unbiased participant (part 2, 3, 4) Bars show standard error.
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_acc ~ GroupType * have_biased + (1 | GroupID)
Data: df_agg
REML criterion at convergence: 2194.1
Scaled residuals:
Min 1Q Median 3Q Max
-3.6009 -0.6198 0.1994 0.7254 2.5621
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 141.6 11.90
Residual 343.6 18.54
Number of obs: 252, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 79.464 5.067 15.010 15.682 1.02e-10 ***
GroupTypeHetero -16.071 7.166 15.010 -2.243 0.04044 *
have_biasedyes 4.762 3.303 236.000 1.442 0.15066
GroupTypeHetero:have_biasedyes -15.179 4.671 236.000 -3.250 0.00132 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH hv_bsd
GroupTypHtr -0.707
have_bisdys -0.326 0.230
GrpTypHtr:_ 0.230 -0.326 -0.707
We also run an extra analysis on the evolution of communicative success, to observe how it evolves within a round. Indeed, as participants are only confronted one time with each image, one could suppose that the communicative success would increase within a round, with an elimination process.
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: ACC ~ InteractionNum * GroupType + (1 | Producer) + (1 | GroupID) +
(1 | Round)
Data: df_agg
REML criterion at convergence: 41453.1
Scaled residuals:
Min 1Q Median 3Q Max
-2.5698 -0.9597 0.2247 0.7487 1.8828
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 154.809 12.442
Round (Intercept) 160.782 12.680
Producer (Intercept) 2.637 1.624
Residual 1679.405 40.981
Number of obs: 4032, groups: GroupID, 14; Round, 9; Producer, 4
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 77.3409 6.6563 22.8132 11.619 4.65e-11
InteractionNum 0.5299 0.1980 4006.6871 2.676 0.00748
GroupTypeHetero -21.9841 7.1807 15.1444 -3.062 0.00784
InteractionNum:GroupTypeHetero -0.1972 0.2800 4005.0007 -0.704 0.48120
(Intercept) ***
InteractionNum **
GroupTypeHetero **
InteractionNum:GroupTypeHetero
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) IntrcN GrpTyH
InteractnNm -0.253
GroupTypHtr -0.539 0.234
IntrctN:GTH 0.179 -0.707 -0.331
Summary results:
Communicative success improves with time (for both groups)
Communicative success is higher in control groups
In heterogeneous groups, communicative success is higher in pairs that do not contain the biased individuals. However, the communicative of this type of pairs is still lower than the one in control groups, which suggests that introducing a biased participant has spread some confusion in the whole group.
In this part, we look at the convergence between all words produced in a round. As a reminder, each round, each participant produce one word for each label. So each round, there are 4 word productions for each labels : convergence will be high if these words are similar (such as kesip, kesup, kesip and kesip) but convergence will be low if these words are very different from each other (for example, kesip, onup, asip and keku).
Convergence is computed the following way:
Calculate the normalized Levenshtein distance between all pairs of words within the set of four words.
Find the average of these distances to obtain a single numerical value for each Round, each Shape, and each Group.
Take the complement of this value, so that the measure of convergence increases when the words are more similar, rather than the opposite.
In other words, \(convergence = 1 - (mean(dis(SetWords)))\) where dis(SetWords) is the pairwaise normalized Levenhstein distance between all words in SetWords.
The plot below includes the production of all participants, including the biased one:
Figure 8. Evolution of convergence with time for each group.
We look at the same plot aggregated by group type:
First, we look at the convergence with all participants:
Figure 9. Same, but aggregated by group.
And we look at the model comparing control and heterogenous groups. This refers to the model 2 of the paper:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: All ~ GroupType * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -316.7
Scaled residuals:
Min 1Q Median 3Q Max
-2.7091 -0.6778 0.0682 0.6382 2.2009
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.010588 0.10290
Residual 0.004724 0.06873
Number of obs: 154, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.956567 0.041561 14.440812 23.016 8.70e-13 ***
GroupTypeHetero -0.328186 0.058777 14.440812 -5.584 6.01e-05 ***
Round2 -0.041340 0.002477 138.000000 -16.690 < 2e-16 ***
GroupTypeHetero:Round2 0.017065 0.003503 138.000000 4.872 2.99e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH Round2
GroupTypHtr -0.707
Round2 -0.298 0.211
GrpTypHt:R2 0.211 -0.298 -0.707
Then, we look at:
Figure 10. Same as above, but distinguishing between hetero with biased and hetero without biased participants.
And we observe a model based on this plot, comparing control, hetero with biased, hetero without biased. This refers to the model 2 bis of the main paper:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_lev_dist ~ TypeGroup * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -459.7
Scaled residuals:
Min 1Q Median 3Q Max
-2.52680 -0.64233 0.08447 0.64197 2.18911
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.011642 0.10790
Residual 0.005428 0.07367
Number of obs: 231, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value
(Intercept) 0.956567 0.043703 14.918711 21.888
TypeGroupHetero With Biased -0.328186 0.061805 14.918711 -5.310
TypeGroupHetero Without Biased -0.254336 0.061805 14.918711 -4.115
Round2 -0.041340 0.002655 213.050677 -15.571
TypeGroupHetero With Biased:Round2 0.017065 0.003755 213.050677 4.545
TypeGroupHetero Without Biased:Round2 0.012387 0.003755 213.050677 3.299
Pr(>|t|)
(Intercept) 9.45e-13 ***
TypeGroupHetero With Biased 8.90e-05 ***
TypeGroupHetero Without Biased 0.000927 ***
Round2 < 2e-16 ***
TypeGroupHetero With Biased:Round2 9.20e-06 ***
TypeGroupHetero Without Biased:Round2 0.001137 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) TypGrpHtrWthBs TypGrpHtrWthtB Round2
TypGrpHtrWthBs -0.707
TypGrpHtrWthtB -0.707 0.935
Round2 -0.304 0.215 0.215
TypeGrpHtrWthBsd:Rnd2 0.215 -0.304 -0.152 -0.707
TypGrpHtrWthtBsd:Rnd2 0.215 -0.152 -0.304 -0.707
TypeGrpHtrWthBsd:Rnd2
TypGrpHtrWthBs
TypGrpHtrWthtB
Round2
TypeGrpHtrWthBsd:Rnd2
TypGrpHtrWthtBsd:Rnd2 0.500
This analysis helps us gain insight into our data. We want to know if participants eventually adopt the initial labels, even if they initially didn’t remember them. To find out, we calculate the average Levenshtein distance between participants’ productions and the initial labels at each round.
Please note that this measure goes against the biased participant, as even if they remember the initial labels correctly, they may not be able to reproduce the exact initial labels.
We look at the evolution of production similarity for each shape:
Figure 11. Evolution of the production similarity at each round, for each shape. Please note that this plot does not include the productions of the biased participant.
To see the production similarity by group:
Figure 12. Evolution of the production similarity at each round, for each shape. Please note that this plot does not include the productions of the biased participant.
We observe that certain shapes are more effectively remembered than others. For instance, “aike” and “nus” are often well-remembered, while “puak” tends to be frequently forgotten.
This plot also reveals that individuals in the control group often converge on the initial labels in the end, even if they initially forget it. However, in the heterogenous group, this convergence does not occur. Participants’ productions tend to become slightly closer to the initial labels, but in the end, the words still remain quite different, even for words that did not contain a biased letter (nus and esip)!
We look at the same plot aggregated by group type. Please note that the following plot is biased, because the biased participant could not produce the exact initial labels. Below, you will find a plot that is more suited to compare control and heterogenous groups.
Figure 13. Same plot as above, but aggregated by shape. Please note that this plot does not include the productions of the biased participant.
Then, we apply a model to compare the two groups, which is refered to as model 3 in the main paper:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_lev_dis ~ GroupType * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -610.4
Scaled residuals:
Min 1Q Median 3Q Max
-3.8445 -0.6126 0.1272 0.6344 3.3697
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.01113 0.1055
Residual 0.01937 0.1392
Number of obs: 616, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.934176 0.042537 14.389325 21.961 1.80e-12 ***
GroupTypeHetero -0.304382 0.060157 14.389325 -5.060 0.00016 ***
Round2 -0.023053 0.002507 600.000001 -9.193 < 2e-16 ***
GroupTypeHetero:Round2 0.014273 0.003546 600.000001 4.025 6.43e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH Round2
GroupTypHtr -0.707
Round2 -0.295 0.208
GrpTypHt:R2 0.208 -0.295 -0.707
Now, we split heterogenous condition in two: participants in heterogenous groups in pairs with (hetero_biased) and without (hetero_unbiased) the biased participant, similarly with previous plots. Is is a better measure since the data from the biased participant is artificially biased.
Figure 14. Same plot as above, except that here, we differentiate between pairs interacting with the biased individuals, and pairs interacting without the biased individual.
We can see that as expected, due to our measure of production similarity, the performance of the biased participant was dragging the whole group to lower similarity. However, we still can find differences between the control groups and the heterogenous groups containing only unbiased participants.
Let’s see if this difference is significant (model 3 bis in the main paper):
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_lev_dis ~ Condition * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -377
Scaled residuals:
Min 1Q Median 3Q Max
-4.0087 -0.6323 0.0673 0.6161 3.4418
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.011787 0.10857
Residual 0.005042 0.07101
Number of obs: 189, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value
(Intercept) 0.953641 0.045431 16.869431 20.991
ConditionHetero With Biased -0.424984 0.064249 16.869431 -6.615
ConditionHetero Without Biased -0.273413 0.064249 16.869431 -4.255
Round2 -0.026245 0.003465 171.069028 -7.575
ConditionHetero With Biased:Round2 0.019480 0.004900 171.069028 3.975
ConditionHetero Without Biased:Round2 0.012143 0.004900 171.069028 2.478
Pr(>|t|)
(Intercept) 1.58e-13 ***
ConditionHetero With Biased 4.56e-06 ***
ConditionHetero Without Biased 0.000542 ***
Round2 2.16e-12 ***
ConditionHetero With Biased:Round2 0.000103 ***
ConditionHetero Without Biased:Round2 0.014178 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) CndtnHtrWthBs CndtnHtrWthtB Round2
CndtnHtrWthBs -0.707
CndtnHtrWthtB -0.707 0.908
Round2 -0.381 0.270 0.270
CondtnHtrWthBsd:Rnd2 0.270 -0.381 -0.191 -0.707
CndtnHtrWthtBsd:Rnd2 0.270 -0.191 -0.381 -0.707
CondtnHtrWthBsd:Rnd2
CndtnHtrWthBs
CndtnHtrWthtB
Round2
CondtnHtrWthBsd:Rnd2
CndtnHtrWthtBsd:Rnd2 0.500
Here, we look at a different index: how similar are the productions from the unbiased participants with the productions from the biased participants. We do this by computing the levenshtein distance between the productions from the unbiased, and the production of the biased used in this round.
We do this for both groups, in order to check, but please note that in control groups we note “Participant 1” (who is unbiased) as the biased participant.
Figure 15. Evolution of the production similarity of unbiased participants with the biased participants.
Figure 16. Same as above, but plotting the linear regression going through the points.
We can see that the participant used terms more and more similar with the labels used by the biased participants. However, the comparison with control groups (in which the biased participant is just Participant 1, i.e. an unbiased participant), suggest that this is not specifically an adaptation to the biased participant, but probably more something related to the fact that participants converge, at least partly, on the initial labels.
Stability is a measure of the levenstein distances between all pairs of words from rounds n and n-1.
First, we look at the evolution of stability for each shape.
To better understand how the function works, let’s take an example for the shape kesip for one group:
Stability is computed by computing the levenshtein distance between all pairs of words (puise and puie, then puise and suki, and so on…). In this case stability between round 7 and 8 for the shape kesip is equal to 0.59.
Since this value assumes that the data is computed between rounds n and n-1, it is normal that the plots shows the value for stability only from round 1 to round 10.
Figure 17. Evolution of stability with time for the group (including biased participants.
We look at the same type of data, except that it is aggregated by group type, similarly as what was performed before.
Figure 18. Evolution of stability with time for the group (excluding biased participants).
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: stab ~ GroupType * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -345.5
Scaled residuals:
Min 1Q Median 3Q Max
-2.37624 -0.59170 -0.02896 0.61681 3.16096
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.009844 0.09922
Residual 0.002886 0.05372
Number of obs: 140, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.944215 0.039354 13.729821 23.993 1.32e-12 ***
GroupTypeHetero -0.278455 0.055655 13.729821 -5.003 0.000205 ***
Round2 -0.035742 0.002235 124.000000 -15.989 < 2e-16 ***
GroupTypeHetero:Round2 0.012773 0.003161 124.000000 4.040 9.30e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH Round2
GroupTypHtr -0.707
Round2 -0.256 0.181
GrpTypHt:R2 0.181 -0.256 -0.707
Figure 19. Evolution of stability aggregated with time for each type of group: everyone (all) or everyone except the biased participant (Without Biased).
And a model:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Stab ~ TypeGroup * Round2 + (1 | GroupID)
Data: df_agg
REML criterion at convergence: -505.1
Scaled residuals:
Min 1Q Median 3Q Max
-3.1921 -0.5972 0.0185 0.6486 3.1799
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.010430 0.10213
Residual 0.003367 0.05803
Number of obs: 210, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value
(Intercept) 0.944215 0.040696 14.179876 23.202
TypeGroupHetero_All -0.278455 0.057552 14.179876 -4.838
TypeGroupHetero_Unbiased -0.211269 0.057552 14.179876 -3.671
Round2 -0.035742 0.002415 192.043738 -14.801
TypeGroupHetero_All:Round2 0.012773 0.003415 192.043738 3.740
TypeGroupHetero_Unbiased:Round2 0.008902 0.003415 192.043738 2.607
Pr(>|t|)
(Intercept) 1.11e-12 ***
TypeGroupHetero_All 0.000254 ***
TypeGroupHetero_Unbiased 0.002470 **
Round2 < 2e-16 ***
TypeGroupHetero_All:Round2 0.000243 ***
TypeGroupHetero_Unbiased:Round2 0.009860 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) TyGH_A TyGH_U Round2 TGH_A:
TypGrpHtr_A -0.707
TypGrpHtr_U -0.707 0.950
Round2 -0.267 0.189 0.189
TypGrH_A:R2 0.189 -0.267 -0.134 -0.707
TypGrH_U:R2 0.189 -0.134 -0.267 -0.707 0.500
In this part, we will look at a set of different models.
First, we will gather the data by group (of course, excluding the production from the biased participant in the heterogenous group). It leads to beautiful and interpretable plots (the ones printed in the main paper). However, we loose some information by averaging the data. In these models, we have only the Group ID as the random factor. Then, we will look at the data for each individuals. The plots are harder to read, but the statistics are more accurate. In the models, we look at the random effects of participants nested within group ID. For each type of data aggregation, we look both at the evolution of the frequency of biased letters across rounds (including round 0 and 10, which are the testing before and after the communication game), and we also make a special focus on the testing moment (first versus last). We tried to add the round or the moment of testing as random slopes, but it led the models not to converge.
To summarize our models, here is what we used:
| Type aggregation | Fixed effect 1 | Fixed effect 2 | Random effects | Plot | Model |
|---|---|---|---|---|---|
| Group | Round | Group Type | Group ID | Figure 2A | model 4a. |
| Group | Testing moment | Group Type | Group ID | Figure 2B | model 4b |
| Individual | Round | Group Type | Group ID / part_ID | not in the main paper | model 4, in the main paper |
| Individual | Testing moment | Group Type | Group ID / part_ID | not in the main paper | model 4c |
Here, we calculate the frequency of biased and unbiased letters. For each round, we determine the total frequency of “k” and “a” out of all the letters used in that round to obtain the frequency of biased letters. Similarly, we compute the frequency of “p”, “n”, “s”, “e”, “i”, and “u” out of the total frequency of letters used in the round to obtain the frequency of unbiased letters. Since there are 6 unbiased letters and 2 biased letters, we divide the frequency of biased letters by 2 and the frequency of unbiased letters by 6.
Please note that the initial labels have slightly more biased letters than unbiased letters. The frequency of each letter in the initial labels (kesip, esip, nus, nusa, aike, puak, nekuki, anap) is:
a e i k n p s u
5 4 4 5 4 4 4 4
Thus, the initial frequency of each biased letter is of 29.41 %.
In all the following plots, we will represent these initial frequencies with a black dashed line.
Figure 20. Plot showing the evolution of frequency of biased letters in control groups (red) and heterogenous groups (blue). Each line represent a group, and the thick line shows the linear regression applied to all these groups.
Out of curiosity, let’s observe if we plot the same plot with a loess regression instead of a linear one:
Figure 21. Same as above, but using loess regression.
Let’s use a linear model to study if there is an effect of time and group type on the frequency of biased and unbiased letters. The model include testing sessions (round 0 to 10), and is refered as model 4a.
Without random slopes for round number:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ Round2 * GroupType + (1 | GroupID)
Data: df_agg
REML criterion at convergence: 739.8
Scaled residuals:
Min 1Q Median 3Q Max
-2.6092 -0.5602 0.0435 0.5250 2.5411
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 12.369 3.517
Residual 5.398 2.323
Number of obs: 154, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 28.90363 1.41858 14.38761 20.375 5.14e-12 ***
Round2 0.00534 0.08373 138.00000 0.064 0.9492
GroupTypeHetero -5.21776 2.00618 14.38761 -2.601 0.0206 *
Round2:GroupTypeHetero 0.48548 0.11841 138.00000 4.100 7.02e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Round2 GrpTyH
Round2 -0.295
GroupTypHtr -0.707 0.209
Rnd2:GrpTyH 0.209 -0.707 -0.295
With random slopes for round number:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ Round2 * GroupType + (1 + Round2 | GroupID)
Data: df_agg
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 715.1
Scaled residuals:
Min 1Q Median 3Q Max
-3.1058 -0.4826 0.0038 0.4949 1.8808
Random effects:
Groups Name Variance Std.Dev. Corr
GroupID (Intercept) 25.6494 5.0645
Round2 0.1215 0.3486 -0.92
Residual 4.2363 2.0582
Number of obs: 154, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 28.90363 1.96386 11.99993 14.718 4.83e-09 ***
Round2 0.00534 0.15119 11.99994 0.035 0.9724
GroupTypeHetero -5.21776 2.77732 11.99993 -1.879 0.0848 .
Round2:GroupTypeHetero 0.48548 0.21381 11.99994 2.271 0.0424 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Round2 GrpTyH
Round2 -0.873
GroupTypHtr -0.707 0.617
Rnd2:GrpTyH 0.617 -0.707 -0.873
The plot and model suggest:
There is more variation in heterogenous groups compared to control groups
In control groups, the proportion of biased and unbiased letters remains similar to the initial frequency of these letters
In heterogenous groups, the proportion of unbiased letters slightly increases with time, while the proportion of biased letters slightly decreases with time.
Let’s look at the same plot, but using aggregated values for all groups:
Figure 22. Same plot as above, aggregated by group number.
Interestingly, the frequency of biased letters dropped at round 3 in heterogenous groups. It could be due to the fact that unbiased participants have been paired with the biased participant successively in round 1 and 2, and thus have both in mind the vocabulary with less biased letters.
The previous plot focused on the evolution of the frequency of biased and unbiased letters across all rounds (0 to 10). Now, we will focus solely on Round 0 and Round 10, namely, the initial (FirstTest, after the passive exposure) and the final testing (LastTest, after the communication game). Here too, we remove the data from the biased participant in the heterogenous groups.
Figure 23. Change in the frequency of biased and unbiased letters in the first testing (before the communication game) and in the second testing (after the communication game) at a group-level. Each point represent a group, and the thin grey line indicate the within design (each group is tested before and after).
We compute the model, which is refered as model 4b (see [2 - Group-adaptation to the biased participants]) for more information. Note that a model with a random slopes for TypeTest did not converge.
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ TypeTest * GroupType + (1 | GroupID)
Data: df_agg
REML criterion at convergence: 131
Scaled residuals:
Min 1Q Median 3Q Max
-1.52681 -0.48572 0.05654 0.30750 2.49407
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 3.794 1.948
Residual 6.833 2.614
Number of obs: 28, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 29.792 1.232 21.287 24.179 <2e-16
TypeTestLast Test -4.484 1.397 12.000 -3.209 0.0075
GroupTypeControl -1.068 1.742 21.287 -0.613 0.5464
TypeTestLast Test:GroupTypeControl 4.051 1.976 12.000 2.050 0.0629
(Intercept) ***
TypeTestLast Test **
GroupTypeControl
TypeTestLast Test:GroupTypeControl .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) TypTLT GrpTyC
TypTstLstTs -0.567
GrpTypCntrl -0.707 0.401
TypTsLT:GTC 0.401 -0.707 -0.567
This is not significant, but it could be due to the low number of groups. Thus, we also perform bootstrapping.
Bootstrapping is a resampling technique used in statistics to estimate the uncertainty associated with a sample statistic. It involves repeatedly drawing random samples with replacement from the original data set. By creating multiple bootstrap samples, the method allows for the estimation of sampling variability, constructing confidence intervals, and assessing the statistical significance of results. Bootstrapping is particularly useful when the sample size is small or when the underlying data distribution is unknown or non-normal, as it provides a robust and flexible approach for inference.
# A tibble: 12 × 6
term estimate lower upper type level
<chr> <dbl> <dbl> <dbl> <chr> <dbl>
1 (Intercept) 29.8 27.1 32.1 norm 0.95
2 GroupTypeControl -1.07 -4.40 2.65 norm 0.95
3 TypeTestLast Test -4.48 -6.89 -1.69 norm 0.95
4 GroupTypeControl:TypeTestLast Test 4.05 -0.0332 8.02 norm 0.95
5 (Intercept) 29.8 27.4 32.2 basic 0.95
6 GroupTypeControl -1.07 -4.25 2.21 basic 0.95
7 TypeTestLast Test -4.48 -6.55 -2.02 basic 0.95
8 GroupTypeControl:TypeTestLast Test 4.05 0.192 7.77 basic 0.95
9 (Intercept) 29.8 27.3 32.2 perc 0.95
10 GroupTypeControl -1.07 -4.35 2.11 perc 0.95
11 TypeTestLast Test -4.48 -6.95 -2.42 perc 0.95
12 GroupTypeControl:TypeTestLast Test 4.05 0.335 7.91 perc 0.95
Figure 24. Estimate of the confident intervals from the Bootstrapping technique. .
When observing the lower and upper bound for the ineraction between GroupType and TypeTest, we found that this confidence interval never includes zero. It is hinting at the possible significance of the data if we have had more groups.
@fig-freq-testing2 also highlights that two groups within the heterogenous condition (Group 2 and Group 6) deviate from this pattern. Our hypothesis is that these groups did not adapt to the biased participant because their participants remembered too well the initial labels, causing them to stick by those words. To further investigate, let’s examine the accuracy of the initial learning phase for all groups:
Figure 25. Investigating more the relation between adaptability and performance at learning the initial words. Here, we look at the initial accuracy (binary, 0 or 1) and the initial distance words (levenshtein distance) in the first testing for each group. We expect the performance to be better for Group 2 and Group 6.
It appears that Group 2 and Group 6 (the groups that did not adapt to the biased participants) also exhibited higher learning accuracy. Let’s verify whether our hypothesis is encouraged by checking if these groups had nearly identical words at the end compared to the initial words.
For group 2:
Before communicating labels:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipe | unup | esip | nesip | nepupi | esu | nusu | puei |
| 2 | aike | upak | esip | kesip | nusa | nusa | nusa | puak |
| 3 | anap | anap | esip | kesip | nekuki | nus | nusa | puak |
| 4 | aike | kusap | esi | kesi | sup | nus | nuk | nuki |
After communicating labels:
| PartID | aike | anap | esip | kesip | nekuki | nus | nusa | puak |
|---|---|---|---|---|---|---|---|---|
| 1 | eipe | unup | esip | nesip | nepupi | nus | nusu | pue |
| 2 | aike | anap | pua | kesip | kukupa | nus | nusa | pua |
| 3 | aike | anap | esip | kesip | nekuki | nus | nusa | pua |
| 4 | aike | anap | esip | kesip | kukupa | nus | nusa | pua |
For Group 6:
Before communicating labels:
| PartID | nusa | nus | kesip | esip | puak | nekuki | anap | aike |
|---|---|---|---|---|---|---|---|---|
| 1 | esei | enep | nuis | senui | nus | nusi | nesupi | |
| 2 | aike | anap | esip | kesip | nekuki | nun | nusa | puak |
| 3 | aike | anap | esip | sekin | nekuki | sap | nusa | puak |
| 4 | peki | ani | sunak | nekaki | nusaki | nuk | nekaki | nusak |
After communicating labels:
| PartID | nusa | nus | kesip | esip | puak | nekuki | anap | aike |
|---|---|---|---|---|---|---|---|---|
| 1 | eipi | enep | epui | puise | pepupi | nuse | nus | epei |
| 2 | aike | anap | seki | kesip | nekuki | nan | nusa | puak |
| 3 | aike | anap | seki | esip | nekuki | nak | nusa | puak |
| 4 | kuap | ani | nekaki | epi | nesaki | suk | peike | kuap |
Let’s see if this is significant:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: mean_acc ~ GroupOK + (1 | GroupNum)
Data: df_agg
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 249.5
Scaled residuals:
Min 1Q Median 3Q Max
-2.17398 -0.79615 0.04701 0.73152 1.45716
Random effects:
Groups Name Variance Std.Dev.
GroupNum (Intercept) 0.0 0.00
Residual 707.2 26.59
Number of obs: 28, groups: GroupNum, 7
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 36.250 5.946 26.000 6.096 1.92e-06 ***
GroupOKDidNotAdapt 21.563 11.125 26.000 1.938 0.0635 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
GrpOKDdNtAd -0.535
optimizer (bobyqa) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
Call:
lm(formula = mean_acc ~ GroupOK, data = df_agg)
Residuals:
Min 1Q Median 3Q Max
-57.81 -21.17 1.25 19.45 38.75
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 36.250 5.946 6.096 1.92e-06 ***
GroupOKDidNotAdapt 21.563 11.125 1.938 0.0635 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 26.59 on 26 degrees of freedom
Multiple R-squared: 0.1263, Adjusted R-squared: 0.09265
F-statistic: 3.757 on 1 and 26 DF, p-value: 0.06352
In order to look more precisely at the relation between learning accuracy and adaptability, please refer to part 3 - Who adapts and when? and subpart Predicting adaptation.
Now, we look at the evolution of the production similarity with the initial labels with time with a focus on these two groups:
Figure 27. Evolution of the production similarity at each round and for each group. Please note that this plot does not include the productions of the biased participant.
This plot helps understand the non adaptability of Group 2 - participants of this group converged on the initial labels. However, no clear explanation emerges about the performance reached by Group 6.
This is the same plot as before, except that we plot here the results for each participant. See the part [2 - Group-adaptation to the biased participants] for more information.
Please note that while we did not printed this plot in the main paper, the model associated to this plot is the one we put in the main paper.
Figure 28. Plot showing the evolution of frequency of biased letters in control groups (red) and heterogenous groups (blue). Each line represent a group, and the thick line shows the linear regression applied to all these groups.
Figure 28. Plot showing the evolution of frequency of biased letters in control groups (red) and heterogenous groups (blue). Each line represent a group, and the thick line shows the linear regression applied to all these groups.
Let’s look at the model, included in the main paper and refered to as model 4. Please note that this model include testing sessions (round 0 to 10). We did not include the round as a random slope.
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ Round2 * GroupType + (1 | GroupID/PartID_unique)
Data: df_agg
REML criterion at convergence: 3054.5
Scaled residuals:
Min 1Q Median 3Q Max
-3.6513 -0.5190 -0.0076 0.5139 4.2969
Random effects:
Groups Name Variance Std.Dev.
PartID_unique:GroupID (Intercept) 4.541 2.131
GroupID (Intercept) 10.630 3.260
Residual 14.059 3.750
Number of obs: 539, groups: PartID_unique:GroupID, 49; GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 28.889341 1.356657 12.697214 21.295 2.58e-11 ***
Round2 0.008185 0.067563 488.000501 0.121 0.9036
GroupTypeHetero -5.176293 1.946370 13.455257 -2.659 0.0192 *
Round2:GroupTypeHetero 0.469077 0.103204 488.000500 4.545 6.93e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Round2 GrpTyH
Round2 -0.249
GroupTypHtr -0.697 0.174
Rnd2:GrpTyH 0.163 -0.655 -0.265
Adding round or round type as random slopes causes the model not to converge:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ Round2 * GroupType + (1 + Round2 | GroupID/PartID_unique)
Data: df_agg
Control: lmerControl(optimizer = "bobyqa")
REML criterion at convergence: 3005.6
Scaled residuals:
Min 1Q Median 3Q Max
-3.9117 -0.4638 0.0175 0.4466 3.8943
Random effects:
Groups Name Variance Std.Dev. Corr
PartID_unique:GroupID (Intercept) 4.5471 2.1324
Round2 0.1386 0.3723 -0.43
GroupID (Intercept) 24.0662 4.9057
Round2 0.1013 0.3183 -1.00
Residual 11.7363 3.4258
Number of obs: 539, groups: PartID_unique:GroupID, 49; GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 28.889341 1.932302 11.442407 14.951 7.3e-09 ***
Round2 0.008185 0.152439 11.257713 0.054 0.9581
GroupTypeHetero -5.176293 2.750667 11.748949 -1.882 0.0849 .
Round2:GroupTypeHetero 0.469077 0.222252 12.597970 2.111 0.0554 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Round2 GrpTyH
Round2 -0.864
GroupTypHtr -0.702 0.607
Rnd2:GrpTyH 0.592 -0.686 -0.849
optimizer (bobyqa) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
This plot is the same as in figure 18, except that we plot here the output for each participant.
Figure 29. Evolution of the mean frequency of biased and unbiased letters for each individual in each group type.
This model is refered as model 4c:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ TypeTest * GroupType + (1 | GroupID/PartID_unique)
Data: df_freq
REML criterion at convergence: 553.6
Scaled residuals:
Min 1Q Median 3Q Max
-1.79806 -0.65303 -0.00725 0.63814 2.11781
Random effects:
Groups Name Variance Std.Dev.
PartID_unique:GroupID (Intercept) 4.131 2.033
GroupID (Intercept) 3.296 1.815
Residual 13.193 3.632
Number of obs: 98, groups: PartID_unique:GroupID, 49; GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 28.7550 1.0438 15.1128 27.548 2.47e-14
TypeTestLast Test -0.4778 0.9707 47.0000 -0.492 0.6249
GroupTypeHetero 1.0060 1.5444 18.1165 0.651 0.5230
TypeTestLast Test:GroupTypeHetero -3.9701 1.4828 47.0000 -2.677 0.0102
(Intercept) ***
TypeTestLast Test
GroupTypeHetero
TypeTestLast Test:GroupTypeHetero *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) TypTLT GrpTyH
TypTstLstTs -0.465
GroupTypHtr -0.676 0.314
TypTsLT:GTH 0.304 -0.655 -0.480
Here too, adding random slopes for TypeTest causes the model not to converge.
Using violin plots and standard errors
Figure 30. Plot showing the evolution of frequency of both biased letters (red) and unbiased letters (blue). Each point represents a participant, and its production at specific moment: with it lasts interaction with a unbiased participant (left panel, left side), and a biased participant (left panel, right side), and during its first testing before communication game (right panel, left side), and during the last testing after communication game (right panel, right side).
Figure 30. Plot showing the evolution of frequency of both biased letters (red) and unbiased letters (blue). Each point represents a participant, and its production at specific moment: with it lasts interaction with a unbiased participant (left panel, left side), and a biased participant (left panel, right side), and during its first testing before communication game (right panel, left side), and during the last testing after communication game (right panel, right side).
We focus here on the pair-level: we compare the productions of the participants in the pair excluding the biased participants (pair 2 - 3, 3 - 4, and 2 - 4) to the production used by pairs involving the biased participant (pair 1 - 2, 1 - 3, and 1 - 4). Important note: the numbers of words considered when omparing between pair without and with the biased participant differ, as we do not consider the productions of Participant 1. For example, in Round 1, we compare the output of:
Pair without the biased participant (Hetero_unbiased): production of participant 3 and participant 4 -> 16 words in total
Pair involving the biased participant (Hetero_biased): production of participant 2 only (we did not look at the frequency of biased letter for participant 1 because this participant is unable to produce any of these letters) -> 8 words in total
Figure 31. Change in the frequency of biased and unbiased letters in the first testing (before the communication game) and in the second testing (after the communication game) at a group-level. Each point represent a group, and the thin grey line indicate the within design (each group is tested before and after).
An interesting observation appears: in Round 3, pairs with unbiased individuals use less biased letters than the unbiased participants involved in the preceding rounds! One hypothesis is that these two unbiased participants have been paired with the biased participant in the preceding rounds and already start to adjust to them.
We merge these results over the rounds, to have a look at the global picture:
Figure 32. Evolution of the mean frequency of biased letters comparing two types of pair: pair including the biased participant (1-2, 1-3, and 1-4) and pair excluding the biased participant (2-3, 3-4, 2-4).
We build two models: one in which the group type is a fixed effect (but please note that this introduces a bias, since in control groups, there is no “talk to bias” or “talk to unbias” - instead, it reflects whether participants 2, 3, and 4 talk to participant1 or not).
This is not the model 5 refered in the main paper, since we also have here the control groups:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ GroupType * TalkToBiased + (1 | GroupID/PartID_unique)
Data: df_agg
REML criterion at convergence: 309.5
Scaled residuals:
Min 1Q Median 3Q Max
-2.26916 -0.38120 -0.03873 0.32515 2.28763
Random effects:
Groups Name Variance Std.Dev.
PartID_unique:GroupID (Intercept) 1.013 1.006
GroupID (Intercept) 2.902 1.704
Residual 1.064 1.031
Number of obs: 84, groups: PartID_unique:GroupID, 42; GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 14.5818 0.7166 13.2669 20.350 2.16e-11
GroupTypeHetero -1.0773 1.0134 13.2669 -1.063 0.306723
TalkToBiasedYes -0.1710 0.3183 40.0000 -0.537 0.594076
GroupTypeHetero:TalkToBiasedYes -1.6846 0.4501 40.0000 -3.742 0.000573
(Intercept) ***
GroupTypeHetero
TalkToBiasedYes
GroupTypeHetero:TalkToBiasedYes ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpTyH TlkTBY
GroupTypHtr -0.707
TalkToBsdYs -0.222 0.157
GrpTyH:TTBY 0.157 -0.222 -0.707
Then, we also look only at heterogeneous groups. This is the model 5 refered in the main paper:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Freq ~ TalkToBiased + (1 | GroupID/PartID_unique)
Data: df_agg
REML criterion at convergence: 171.5
Scaled residuals:
Min 1Q Median 3Q Max
-1.91303 -0.32334 -0.08062 0.29827 1.78595
Random effects:
Groups Name Variance Std.Dev.
PartID_unique:GroupID (Intercept) 1.757 1.326
GroupID (Intercept) 5.415 2.327
Residual 1.470 1.212
Number of obs: 42, groups: PartID_unique:GroupID, 21; GroupID, 7
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 13.5046 0.9630 6.4768 14.02 4.35e-06 ***
TalkToBiasedYes -1.8556 0.3741 20.0000 -4.96 7.54e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
TalkToBsdYs -0.194
We compute three measures of adaptability based on the ratio of letter frequency:
Adapt1. The first one reflects, for each participant, the difference between the frequency of biased letter in the FirstTesting and the frequency of biased letter in the SecondTesting. A larger number indicates a greater decrease in the number of biased letters in the participants’ final vocabulary (so the participant adapted to the peculiarities of the biased participant). Conversely, a negative score for adaptability means that the person has increased the number of biased letters (so the participant did not adapt to the peculiarities of the biased participant).
Adapt2. The measure is very similar to the first one, except that here we do not look at the First and Second Testing, but at all interactions with the biased participants made from Round 1 to 9.
Adapt3. This measure is the most complex, and the most likely to efficiently represent adaptability. We arbitrarily created a score based on a decision tree, see image below:
Adapt4. This is similar to Adapt3, except that here, we look at the normalized distance between:
d1: the new item produced and the item the partner has said
d2: the new item produced and the last item produced by the participant.
Then, we computed the Adapt4 as 2*(1-d1) + d2 (see below)
We look at this only in heterogenous groups for Adapt1 and Adapt2, and for both groups (heterogeneous and control) in Adapt3.
Do these measures correlate with each other, and how are they distributed?
Figure 34. Correlation between the adaptability scores.
The correlation between the measure for Adaptability 1 and 2 is quite low, while it should be higher.
However, we will still try to observe how our different metrics (such as age, gender…: see Method) correlate with the adaptability scores. First, we look at the variable distribution.
Figure 35. Distribution of the scores. Red shows the results for the control group, blue shows the results for the heterogenous group.
Just a reminder:
Let’s look at the correlations between the numerical variables:
Figure 36. Correlation between the predictors.
But, in order to see more clearly (and also add the effect of gender, which we could not see in the plot above, we will have a closer look at each of our Adaptability measures.
We first look at the measure using the score of Adaptability1:
(please note that this variable only includes participants from heterogenous groups)
Figure 37. Correlations between the different individual measures and our score for Adaptability1. Reminder: in the dictator game 1 is keeping all the money for oneself, 5 is to share it all.
Model:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability1 ~ prosoc_z + WorkingMem_z + CogFlexibility_z +
DictatorGame_z + Age_z + Gender_z + AccLearning_z + ProducSim_z +
(1 | GroupNum)
Data: df_other2_z
REML criterion at convergence: 94.1
Scaled residuals:
Min 1Q Median 3Q Max
-1.19689 -0.50159 -0.08027 0.57271 0.91707
Random effects:
Groups Name Variance Std.Dev.
GroupNum (Intercept) 31.66 5.627
Residual 30.88 5.557
Number of obs: 21, groups: GroupNum, 7
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.1033 2.7219 3.5991 1.507 0.214
prosoc_z -3.8259 4.4046 10.6155 -0.869 0.404
WorkingMem_z 1.5921 4.6609 11.9684 0.342 0.739
CogFlexibility_z -1.5782 6.3158 8.2278 -0.250 0.809
DictatorGame_z -2.0221 2.0809 11.7485 -0.972 0.351
Age_z -0.2419 0.5957 11.3888 -0.406 0.692
Gender_z -0.1714 4.3611 6.9454 -0.039 0.970
AccLearning_z -8.2086 17.1805 9.7835 -0.478 0.643
ProducSim_z 10.6719 22.3196 10.7742 0.478 0.642
Correlation of Fixed Effects:
(Intr) prsc_z WrknM_ CgFlx_ DcttG_ Age_z Gndr_z AccLr_
prosoc_z 0.224
WorkingMm_z -0.165 -0.294
CgFlxblty_z -0.032 0.181 0.416
DictatrGm_z 0.132 0.206 -0.352 -0.171
Age_z 0.240 0.735 -0.064 0.239 -0.070
Gender_z -0.396 -0.540 0.436 0.016 -0.077 -0.580
AccLernng_z 0.034 0.036 0.393 0.113 0.110 0.169 0.254
ProducSim_z -0.085 -0.231 -0.071 -0.003 -0.144 -0.295 -0.045 -0.892
R2m R2c
[1,] 0.06919029 0.5404263
R²m focuses solely on the fixed effects’ contribution to explaining variance, while R²c takes into account both the fixed effects and the random effects.
We look at the exact same plots using the score for Adaptability2:
Figure 38. Correlations between the different individual measures and our score for Adaptability2. Reminder: in the dictator game 1 is keeping all the money for oneself, 5 is to share it all.
Model:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability1 ~ prosoc_z + WorkingMem_z + CogFlexibility_z +
DictatorGame_z + Age_z + Gender_z + AccLearning_z + ProducSim_z +
(1 | GroupID)
Data: df_other2_z
REML criterion at convergence: 94.1
Scaled residuals:
Min 1Q Median 3Q Max
-1.19689 -0.50159 -0.08027 0.57271 0.91707
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 31.66 5.627
Residual 30.88 5.557
Number of obs: 21, groups: GroupID, 7
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.1033 2.7219 3.5991 1.507 0.214
prosoc_z -3.8259 4.4046 10.6155 -0.869 0.404
WorkingMem_z 1.5921 4.6609 11.9684 0.342 0.739
CogFlexibility_z -1.5782 6.3158 8.2278 -0.250 0.809
DictatorGame_z -2.0221 2.0809 11.7485 -0.972 0.351
Age_z -0.2419 0.5957 11.3888 -0.406 0.692
Gender_z -0.1714 4.3611 6.9454 -0.039 0.970
AccLearning_z -8.2086 17.1805 9.7835 -0.478 0.643
ProducSim_z 10.6719 22.3196 10.7742 0.478 0.642
Correlation of Fixed Effects:
(Intr) prsc_z WrknM_ CgFlx_ DcttG_ Age_z Gndr_z AccLr_
prosoc_z 0.224
WorkingMm_z -0.165 -0.294
CgFlxblty_z -0.032 0.181 0.416
DictatrGm_z 0.132 0.206 -0.352 -0.171
Age_z 0.240 0.735 -0.064 0.239 -0.070
Gender_z -0.396 -0.540 0.436 0.016 -0.077 -0.580
AccLernng_z 0.034 0.036 0.393 0.113 0.110 0.169 0.254
ProducSim_z -0.085 -0.231 -0.071 -0.003 -0.144 -0.295 -0.045 -0.892
R2m R2c
[1,] 0.06919029 0.5404263
We look at the exact same plots using the score for Adaptability3:
Figure 39. Correlations between the different individual measures and our score for Adaptability3. Reminder: in the dictator game 1 is keeping all the money for oneself, 5 is to share it all.
Model, including production from the biased participant:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability2 ~ prosoc_z + WorkingMem_z + CogFlexibility_z +
DictatorGame_z + Age_z + Gender_z + AccLearning_z + ProducSim_z +
(1 | GroupID)
Data: df_other_z
REML criterion at convergence: 75.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.29011 -0.44312 -0.05865 0.32637 1.59578
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.0 0.000
Residual 10.7 3.271
Number of obs: 21, groups: GroupID, 7
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.29736 0.97015 12.00000 3.399 0.00528 **
prosoc_z -1.85364 2.05854 12.00000 -0.900 0.38559
WorkingMem_z 1.57906 1.97838 12.00000 0.798 0.44029
CogFlexibility_z 0.41123 3.21404 12.00000 0.128 0.90031
DictatorGame_z -1.41578 0.95146 12.00000 -1.488 0.16255
Age_z 0.03073 0.28080 12.00000 0.109 0.91465
Gender_z -0.33332 2.28204 12.00000 -0.146 0.88630
AccLearning_z -17.20183 8.33325 12.00000 -2.064 0.06131 .
ProducSim_z 25.30525 10.46976 12.00000 2.417 0.03250 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsc_z WrknM_ CgFlx_ DcttG_ Age_z Gndr_z AccLr_
prosoc_z 0.332
WorkingMm_z -0.216 -0.200
CgFlxblty_z 0.029 0.318 0.238
DictatrGm_z 0.245 0.283 -0.201 -0.062
Age_z 0.425 0.750 -0.093 0.265 0.259
Gender_z -0.612 -0.522 0.354 -0.165 -0.124 -0.631
AccLernng_z 0.135 -0.061 0.230 -0.156 0.316 0.074 0.178
ProducSim_z -0.169 -0.003 0.024 0.212 -0.303 -0.119 -0.043 -0.911
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
R2m R2c
[1,] 0.3327252 0.3327252
Model, excluding production from the biased participant:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability3 ~ prosoc_z + WorkingMem_z + CogFlexibility_z +
DictatorGame_z + Age_z + Gender_z + AccLearning_z + ProducSim_z +
(1 | GroupID)
Data: df_other_z[!(df_other_z$PartID == 1 & df_other_z$GroupType ==
"Hetero"), ]
REML criterion at convergence: -33
Scaled residuals:
Min 1Q Median 3Q Max
-1.57561 -0.51577 -0.07565 0.64390 1.84356
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.003468 0.05889
Residual 0.012497 0.11179
Number of obs: 49, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.1026441 0.0262396 17.1561746 -3.912 0.00111 **
prosoc_z 0.0303311 0.0350553 35.9406462 0.865 0.39265
WorkingMem_z -0.0475077 0.0425451 38.0386109 -1.117 0.27115
CogFlexibility_z 0.0618350 0.0916649 35.7784849 0.675 0.50428
DictatorGame_z 0.0009374 0.0272844 39.0750590 0.034 0.97277
Age_z 0.0005543 0.0041543 39.2380299 0.133 0.89453
Gender_z 0.0286825 0.0401149 35.0562824 0.715 0.47934
AccLearning_z 0.0452152 0.1827187 37.6833403 0.247 0.80590
ProducSim_z 0.0260163 0.2379260 38.4265997 0.109 0.91350
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsc_z WrknM_ CgFlx_ DcttG_ Age_z Gndr_z AccLr_
prosoc_z -0.054
WorkingMm_z 0.046 0.102
CgFlxblty_z -0.028 0.260 0.214
DictatrGm_z 0.033 -0.045 -0.069 -0.092
Age_z 0.148 0.084 0.041 -0.013 -0.186
Gender_z -0.473 0.106 -0.058 0.038 0.038 -0.218
AccLernng_z 0.090 -0.112 0.217 -0.008 0.210 -0.004 0.201
ProducSim_z -0.139 0.136 -0.043 0.038 -0.106 -0.035 -0.119 -0.908
R2m R2c
[1,] 0.0898214 0.2875562
We look at the exact same plots using the score for Adaptability4:
Figure 40. Correlations between the different individual measures and our score for Adaptability4. Reminder: in the dictator game 1 is keeping all the money for oneself, 5 is to share it all.
Model including the production from the biased participant:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability4 ~ prosoc_z + WorkingMem_z + CogFlexibility_z +
DictatorGame_z + Age_z + Gender_z + AccLearning_z + ProducSim_z +
(1 | GroupID)
Data: df_other_z
REML criterion at convergence: 2.3
Scaled residuals:
Min 1Q Median 3Q Max
-1.97671 -0.52383 0.09248 0.63485 1.72760
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.02724 0.1650
Residual 0.02452 0.1566
Number of obs: 56, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 1.6743796 0.0520384 15.3073297 32.176 1.77e-15 ***
prosoc_z -0.0215632 0.0484942 38.5936249 -0.445 0.6591
WorkingMem_z 0.0124828 0.0564002 41.9955380 0.221 0.8259
CogFlexibility_z -0.0007215 0.1263691 37.2664798 -0.006 0.9955
DictatorGame_z -0.0082334 0.0395368 41.4556476 -0.208 0.8361
Age_z -0.0017282 0.0051478 37.4816895 -0.336 0.7390
Gender_z 0.0053707 0.0560555 39.1659955 0.096 0.9242
AccLearning_z -0.3796356 0.1880709 39.5658058 -2.019 0.0503 .
ProducSim_z 0.5098609 0.2441742 39.2527811 2.088 0.0433 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prsc_z WrknM_ CgFlx_ DcttG_ Age_z Gndr_z AccLr_
prosoc_z -0.051
WorkingMm_z 0.002 0.121
CgFlxblty_z -0.031 0.203 0.334
DictatrGm_z 0.013 0.032 -0.073 -0.069
Age_z 0.016 -0.036 -0.121 -0.033 -0.156
Gender_z -0.346 0.148 -0.005 0.088 -0.038 -0.046
AccLernng_z -0.086 -0.132 0.188 0.115 0.127 -0.149 0.247
ProducSim_z 0.042 0.188 0.008 -0.048 0.027 0.093 -0.122 -0.839
R2m R2c
[1,] 0.06788929 0.5583678
prosoc_z WorkingMem_z CogFlexibility_z DictatorGame_z
1.130551 1.362975 1.178453 1.182312
Age_z Gender_z AccLearning_z ProducSim_z
1.058726 1.176554 4.852170 4.322597
Model excluding productions from the biased participants in heterogenous groups:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Adaptability4 ~ prosoc + WorkingMem + CogFlexibility + DictatorGame +
Age + Gender + AccLearning + ProducSim + (1 | GroupID)
Data: df_other_z[!(df_other_z$PartID == 1 & df_other_z$GroupType ==
"Hetero"), ]
REML criterion at convergence: -1.8
Scaled residuals:
Min 1Q Median 3Q Max
-1.53369 -0.62004 0.06346 0.62015 1.46774
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.02709 0.1646
Residual 0.01983 0.1408
Number of obs: 49, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 1.9164854 0.3047512 31.0000785 6.289 5.41e-07 ***
prosoc -0.0271676 0.0466917 30.8501940 -0.582 0.565
WorkingMem -0.0284118 0.0574314 31.5309274 -0.495 0.624
CogFlexibility 0.0175435 0.1218276 30.6041833 0.144 0.886
DictatorGame 0.0037392 0.0394754 36.7633587 0.095 0.925
Age -0.0004194 0.0057419 33.9505566 -0.073 0.942
GenderM 0.0248748 0.0530205 30.1769781 0.469 0.642
AccLearning 0.0290540 0.2463463 31.5907232 0.118 0.907
ProducSim -0.1360715 0.3232488 32.1749557 -0.421 0.677
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) prosoc WrkngM CgFlxb DcttrG Age GendrM AccLrn
prosoc -0.677
WorkingMem -0.447 0.095
CogFlexblty -0.330 0.271 0.228
DictatorGam -0.211 -0.013 -0.078 -0.081
Age -0.335 0.030 0.049 -0.017 -0.274
GenderM -0.025 0.099 -0.063 0.054 0.057 -0.164
AccLearning 0.127 -0.063 0.213 0.040 0.216 0.019 0.229
ProducSim -0.324 0.078 -0.037 -0.007 -0.091 -0.063 -0.152 -0.908
R2m R2c
[1,] 0.0167854 0.5844647
prosoc WorkingMem CogFlexibility DictatorGame Age
1.110681 1.436756 1.140272 1.312834 1.131158
Gender AccLearning ProducSim
1.180877 9.059043 7.886534
Let’s have a look at how the Adaptability score of participants evolve with time:
Let’s observe whether a higher adaptability correlates with a better communicative success in average:
It appears that communicative success is correlated with each participant’s adaptability scores. Is this relationship significant? To determine whether to use a Spearman or Pearson correlation test, we first assess whether the relationship between the two variables is linear. Since both a linear and quadratic model fit the data equally well, we applied both Pearson and Spearman correlation tests.
Pearson's product-moment correlation
data: df_cor$CommunicativeSuccess and df_cor$Adaptability4
t = 4.4871, df = 54, p-value = 3.82e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.2992439 0.6895684
sample estimates:
cor
0.5211453
Spearman's rank correlation rho
data: df_cor$CommunicativeSuccess and df_cor$Adaptability4
S = 14529, p-value = 7.647e-05
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
0.5034611
Now, we want to analyze whether the communicative success has also positively impacted the measures of prosociality, since these measures were performed after the main experiment, maybe it had an effect.
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: prosoc ~ MeanComSuccess + (1 | GroupID)
Data: df_both2
REML criterion at convergence: 89.6
Scaled residuals:
Min 1Q Median 3Q Max
-3.4324 -0.3436 0.0968 0.6252 1.3861
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.02683 0.1638
Residual 0.26187 0.5117
Number of obs: 56, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.74048 0.32618 16.17875 11.467 3.5e-09 ***
MeanComSuccess -0.03742 0.45121 16.49485 -0.083 0.935
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
MeanCmSccss -0.969
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: DictatorGame ~ MeanComSuccess + (1 | GroupID)
Data: df_both2
REML criterion at convergence: 114.4
Scaled residuals:
Min 1Q Median 3Q Max
-2.69756 0.02422 0.23531 0.33410 2.92745
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.08226 0.2868
Residual 0.38975 0.6243
Number of obs: 56, groups: GroupID, 14
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.2857 0.4461 16.3870 7.366 1.38e-06 ***
MeanComSuccess -0.7142 0.6162 16.8276 -1.159 0.263
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
MeanCmSccss -0.967
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: prosoc ~ ACC + (1 | PartID) + (1 | GroupID)
Data: df3
REML criterion at convergence: 10103.3
Scaled residuals:
Min 1Q Median 3Q Max
-2.95153 -0.52747 0.09698 0.72228 1.89562
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.085799 0.29292
PartID (Intercept) 0.008744 0.09351
Residual 0.189610 0.43544
Number of obs: 8512, groups: GroupID, 14; PartID, 4
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 3.715e+00 9.161e-02 1.553e+01 40.555 <2e-16 ***
ACC -1.492e-03 1.088e-02 8.501e+03 -0.137 0.891
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
ACC -0.082
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: DictatorGame ~ ACC + (1 | PartID) + (1 | GroupID)
Data: df3
REML criterion at convergence: 13961.5
Scaled residuals:
Min 1Q Median 3Q Max
-2.67391 -0.19398 0.06182 0.34439 2.66996
Random effects:
Groups Name Variance Std.Dev.
GroupID (Intercept) 0.160969 0.40121
PartID (Intercept) 0.006625 0.08139
Residual 0.298369 0.54623
Number of obs: 8512, groups: GroupID, 14; PartID, 4
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 2.82868 0.11523 15.76121 24.549 5.52e-14 ***
ACC -0.06245 0.01365 8500.42792 -4.575 4.83e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
ACC -0.082
Figure 41. Figure 1 paper
Figure 43. Figure 2 paper.